Theorem 2.6 (Araya and Yoshino [1]}) Assume \(R\)  is a local ring and \(M, N\in \operatorname{mod}(R)\) . If \(\operatorname{\textnormal {CI-dim}}_R(M)<\infty \)  and \(\operatorname{Tor}_i^R(M,N)=0\)  for all \(i\ge 1\) , then \((M,N)\)  satisfies the depth formula; see [1]}.

